Is there a specific term for meteorology on other planets?

Not a single word, but planetary meteorology seems to fit the bill (as opposed to terrestrial meteorology). It requires some particular reading of the words though (ie, planetary to mean non-Earth planets, and terrestrial to mean Earth), but it has been done. See, for example, https://global.jaxa.jp/article/special/explore/imamura02_e.html

Japan is one of the leading countries in the field of terrestrial meteorology. With that background, I believe that we can lead the research of planetary meteorology as well.

Another candidate is extra-terrestrial meteorology. See, for example, https://www.worldcat.org/title/horizon-the-weirdest-weather-in-the-universe/oclc/1089752078

Now scientists have started looking to the heavens and wondering what the weather might be like on other planets. Today, we are witnessing the birth of extra-terrestrial meteorology, as technology is allowing astronomers to study the weather on other planets like never before.

Or https://www.scisnack.com/2017/10/17/meteorology-is-out-of-this-world-extra-terrestrial-meteorology/

So just as investigating Earthly weather can tell us about processes occurring on other planets, delving into extra-terrestrial meteorology can shed some light on how our own atmosphere does, or does not behave.